where \(k\)  is a parametric distribution (for our purposes constrained to the positive orthant) and \(\mathbf {w}=\left\lbrace  w_{1},w_{2},\dots \right\rbrace \)  is the the stick-breaking weight process, here represented using the notation \(\mathbf {w}\sim GEM\left(\alpha \right)\)  (that stands for Griffiths, Engen, McCloskey), as used in [1]} and [2]}. Therefore this approach bypasses the problem of choosing the correct number of components.
Furthermore, [3]} establish the large support property, or adequacy, of DPM, in that a parametric Bayesian model can be approximated by a nonparametric Bayesian model with a mixture of DPs, with the prior assigning most of its weight to neighborhoods of the parametric model, and show that any parametric or nonparametric prior may be approximated arbitrarily closely by a prior which is a mixture of DPs. See also [4]} for similar results on mixture processes of DPs. Corollary 2.2 of [5]} also supports the idea that the model under consideration has a wide applicability to various mispecifications in the generating process.
